Rosette
A really easy bit of etymology
In the world of fretted instruments, any decoration around a circular or oval soundhole is called a "rosette."
Why "rosette" you ask? It's a simple diminutive.
The decoration found covering the soundholes of instruments belonging to the lute family is called a "rose."
Here's a lute rose:
The classical guitar usually has an inlaid rosette made of many little colored wood pieces laid up as a mosaic:
In the world of steel string guitars the most distinctive rosette is the Martin ring design, which dates from before the Civil War:
This one is a Martin 0-28 with a Koa top from about 1927.